physics 101 le3 reviewer (1).pdf

Physics 101 LE3 Reviewer

1. (Tipler 11.95 modified) The force exerted by the earth on a particle of mass m at a distance r from

the center of the earth has the magnitude GMEmr2 =mgR2Er2 .

(a) Calculate the work you must do against gravity to move the particle from a distance r1 to r2.

(b) Show that to go to a height h RE , the potential energy to exert is U = mgh2. The gravitational potential is defined as = z ~g d~r.

(a) Find the gravitational potential exerted by a ring of radius R and constant linear density to a point z above its axis. (See Figure 1a)

(b) Using this result, find the gravitational potential exerted by a disk of radius R with constantsurface density to a point z above its axis. (See Figure 1b)

(c) Using this result, find the gravitational potential exerted by a solid sphere of radius R wihconstant volume density to a point z from its center. (See Figure 1c)

Figure 1: Problem 2

3. Disregard.

4. (Tipler 12.81) A cube of mass M and edge length a leans against a frictionless wall making anangle with the floor as shown in Figure 2. Find the minimum coefficient of static friction Sbetween the cube and the floor that allows the cube to stay at rest.

Figure 2: Problem 4

5. (Tipler 12.89 modified) A thin rod of length L is balanced a distance d from one end when a mass(2m + 2) is at the end nearest the pivot and a mass m is at the opposite end (See Figure 3a).Balance is again achieved if a mass m replaces the mass (2m + 2) at the nearer end and no massis put at the opposite end (See Figure 3b). Determine the mass of the rod.

6. (Univ. Phys. 11.98) Bulk Modulus of an Ideal Gas. The equation of state for an ideal gas ispV = nRT , where n,R = constant.

(a) Show that if the gas is compressed while T = constant, B = p.

(b) When an ideal gas is compressed without transfer of any heat into or out of it, the pressureand volume are related by pV = constant, where varies for every gas. Show that B = p.

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Figure 3: Problem 5

7. (Univ. Phys. 14.86 modified) The horizontal pipe shown in the figure has a cross sectional area of4A at the wider portions and A at the constriction (See Figure 4). Water is flowing in the pipeand it has a discharge rate of r.

(a) Find the flow speeds at the wide and narrow portions.

(b) Find the pressure difference between these portions.

(c) Find the difference in height between mercury columns in the U-shaped tube (suppose water, mercury =constant.

Figure 4: Problem 7

8. (Univ. Phys. 13.88) A slender, uniform, metal rod with mass M is pivoted without friction aboutan axis through its midpoint and perpendicular to the rod. A horizontal spring with force constantk is attached to a lower end of the rod, with the other end of the spring attached to a rigid support.If the rod is displaced by a small angle from the vertical and released, show that it moves inan angular simple harmonic motion and calculate the period (Hint: Assume that is very smallfor the small angle approximations sin and cos 1 to be valid. It is of simple harmonicmotion if d

2dt2 = 2 and T = 2pi .

Figure 5: Problem 8

9. (Univ. Phys. 13.101) Resonance in a Mechanical System. A mass m is attached to a masslessspring with a force constant k and an unstretched length l0. The other end of the spring is freeto turn about a nail driver into a frictionless, horizontal surface with an angular frequency ofrevolution .

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Figure 6: Problem 9

(a) Express l as a function of .

(b) What happens when =

km?

10. (Univ. Phys. 16.63 modified) Masashi blindfolds Kamijo and ties him in front of the car of theDescendants of the Rose. Yuki then drives the car at a speed vK and has him bump straight to awall with a resonant frequency fr,wall. However, Kamijo decides to sing in order to ease his tension.

(a) What is the minimum frequency at which Kamijo should such that the wall crumbles down?

(b) What frequency will he hear his voice reflected from the wall before it crumbles down?

11. Disregard. Incomplete given.

12. Suppose you fire a ray of light at a direction ~v = c sin cosx+ c sin siny+ c cos z, wherein isthe angle between the x-axis and xy-plane projection of the vector and is the angle between thez-axis and the vector. Prove that the speed of light is still c no matter at which frame of referenceit is observed.

Figure 7: Problem 12

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